On the upper limit of percolation threshold in square lattice
Yu.P.Virchenko, Yu.A.Tolmacheva
TL;DR
This paper investigates the maximum possible percolation threshold in a square lattice by estimating the number of external boundary contours of finite clusters, leading to a more precise upper limit.
Contribution
It introduces a geometric estimation method for the number of boundary contours, refining the upper limit of the percolation threshold in square lattices.
Findings
Estimated the number of boundary contours of finite clusters
Determined a more precise upper limit for the percolation threshold
Enhanced understanding of percolation properties in square lattices
Abstract
The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more precisely the upper limit for the percolation threshold.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · advanced mathematical theories